How do you model a spring and damper in series?

[cstoos]

I was wondering about something, and after a quick search through the forums didn't provide an answer I figured I would ask.

So in modeling a spring-mass-damper system, if you have a spring and damper in series, how do you represent that? Do you have to introduce another variable, say y, at a point between the spring and damper?

I am attaching a (crude) drawing of a system that I just made up. If I were to model it like this, would that be correct?

M\ddot{x} - b\dot{y} - k1(x-y)-k2x = 0

It seems right, but this would make it impossible to solve, since y would be considered an independent variable. Should I place and arbitrary mass at y so that I can have two DEs?


(P.S. I couldn't get the subscripts to work properly.)

 

[cstoos]

I have been out of the office for a few days. So, does the lack of response mean that nobody knows or that the solution I presented is accurate?

Edit: This is in no way a homework problem. Just curiousity.